An exact computation of five-loop diagrams with two mass scales (\(m_b\)  and \(m_c\) ) is out
of range using current methods.
We obtain finite charm mass effects by performing an asymptotic expansion
in the parameter \(\delta = 1-m_c/m_b \ll 1\) ,
i.e. we expand the Feynman diagrams around the equal mass limit \(m_c \simeq m_b\) ,
which we realize with the method of regions [1]}, [2]}.
We call this approach the \(\delta \) -expansion.
The opposite limit \(\rho = m_c/m_b \ll 1\)  (the \(\rho \) -expansion) was adopted
in [3]} for the evaluation of the width to \(O(\alpha _s^2)\) .
